LMFDB - Embedded newform 441.4.p.a.215.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(80,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.80");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.9948826238976.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 36x^{6} + 935x^{4} + 12996x^{2} + 130321 $ x^8 + 36x^6 + 935x^4 + 12996*x^2 + 130321
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			215.3
Root			$1.53821 - 4.07847i$ of defining polynomial
Character	$\chi$	$=$	441.215
Dual form			441.4.p.a.80.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 + 1.41421i) q^{2} +(-10.5357 + 18.2483i) q^{5} -22.6274i q^{8} +O(q^{10})$	\(q+(2.44949 + 1.41421i) q^{2} +(-10.5357 + 18.2483i) q^{5} -22.6274i q^{8} +(-51.6140 + 29.7993i) q^{10} +(-13.4722 + 7.77817i) q^{11} -29.7993i q^{13} +(32.0000 - 55.4256i) q^{16} +(31.6070 + 54.7449i) q^{17} +(-77.4209 - 44.6990i) q^{19} -44.0000 q^{22} +(-67.3610 - 38.8909i) q^{23} +(-159.500 - 276.262i) q^{25} +(42.1426 - 72.9932i) q^{26} -125.865i q^{29} +(206.456 - 119.197i) q^{31} +178.796i q^{34} +(92.0000 - 159.349i) q^{37} +(-126.428 - 218.979i) q^{38} +(412.912 + 238.395i) q^{40} -105.357 q^{41} -190.000 q^{43} +(-110.000 - 190.526i) q^{46} +(-21.0713 + 36.4966i) q^{47} -902.268i q^{50} +(309.860 - 178.898i) q^{53} -327.793i q^{55} +(178.000 - 308.305i) q^{58} +(-42.1426 - 72.9932i) q^{59} +(-567.753 - 327.793i) q^{61} +674.282 q^{62} -512.000 q^{64} +(543.787 + 313.955i) q^{65} +(-148.000 - 256.344i) q^{67} -329.512i q^{71} +(-696.788 + 402.291i) q^{73} +(450.706 - 260.215i) q^{74} +(-418.000 + 723.997i) q^{79} +(674.282 + 1167.89i) q^{80} +(-258.070 - 148.997i) q^{82} -1222.14 q^{83} -1332.00 q^{85} +(-465.403 - 268.701i) q^{86} +(176.000 + 304.841i) q^{88} +(-347.677 + 602.193i) q^{89} +(-103.228 + 59.5987i) q^{94} +(1631.36 - 941.866i) q^{95} +566.187i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 256 q^{16} - 352 q^{22} - 1276 q^{25} + 736 q^{37} - 1520 q^{43} - 880 q^{46} + 1424 q^{58} - 4096 q^{64} - 1184 q^{67} - 3344 q^{79} - 10656 q^{85} + 1408 q^{88}+O(q^{100}) $ 8 * q + 256 * q^16 - 352 * q^22 - 1276 * q^25 + 736 * q^37 - 1520 * q^43 - 880 * q^46 + 1424 * q^58 - 4096 * q^64 - 1184 * q^67 - 3344 * q^79 - 10656 * q^85 + 1408 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.44949	+	1.41421i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$2$	2.44949	+	1.41421i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−10.5357	+	18.2483i	−0.942338	+	1.63218i	−0.181341	+	0.983420i	$0.558044\pi$
$5$	−10.5357	+	18.2483i	−0.942338	+	1.63218i	−0.760996	+	0.648756i	$0.775289\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	22.6274i		−	1.00000i
$9$		0			0
$10$	−51.6140	+	29.7993i	−1.63218	+	0.942338i
$11$	−13.4722	+	7.77817i	−0.369274	+	0.213201i	−0.673141	−	0.739514i	$-0.735055\pi$
$11$	−13.4722	+	7.77817i	−0.369274	+	0.213201i	0.303867	+	0.952714i	$0.401722\pi$
$12$		0			0
$13$		−	29.7993i		−	0.635757i	−0.948131	−	0.317879i	$-0.897030\pi$
$13$		−	29.7993i		−	0.635757i	0.948131	−	0.317879i	$-0.102970\pi$
$14$		0			0
$15$		0			0
$16$	32.0000	−	55.4256i	0.500000	−	0.866025i
$17$	31.6070	+	54.7449i	0.450930	+	0.781034i	0.998444	−	0.0557626i	$-0.0177590\pi$
$17$	31.6070	+	54.7449i	0.450930	+	0.781034i	−0.547514	+	0.836797i	$0.684426\pi$
$18$		0			0
$19$	−77.4209	−	44.6990i	−0.934820	−	0.539719i	−0.0464872	−	0.998919i	$-0.514803\pi$
$19$	−77.4209	−	44.6990i	−0.934820	−	0.539719i	−0.888333	+	0.459200i	$0.848136\pi$
$20$		0			0
$21$		0			0
$22$	−44.0000			−0.426401
$23$	−67.3610	−	38.8909i	−0.610684	−	0.352579i	0.162549	−	0.986700i	$-0.448028\pi$
$23$	−67.3610	−	38.8909i	−0.610684	−	0.352579i	−0.773233	+	0.634122i	$0.781362\pi$
$24$		0			0
$25$	−159.500	−	276.262i	−1.27600	−	2.21010i
$26$	42.1426	−	72.9932i	0.317879	−	0.550582i
$27$		0			0
$28$		0			0
$29$		−	125.865i		−	0.805950i	−0.915211	−	0.402975i	$-0.867976\pi$
$29$		−	125.865i		−	0.805950i	0.915211	−	0.402975i	$-0.132024\pi$
$30$		0			0
$31$	206.456	−	119.197i	1.19615	−	0.690596i	0.236453	−	0.971643i	$-0.424015\pi$
$31$	206.456	−	119.197i	1.19615	−	0.690596i	0.959694	+	0.281047i	$0.0906817\pi$
$32$		0			0
$33$		0			0
$34$			178.796i			0.901860i
$35$		0			0
$36$		0			0
$37$	92.0000	−	159.349i	0.408776	−	0.708021i	−0.585977	−	0.810328i	$-0.699289\pi$
$37$	92.0000	−	159.349i	0.408776	−	0.708021i	0.994753	+	0.102307i	$0.0326224\pi$
$38$	−126.428	−	218.979i	−0.539719	−	0.934820i
$39$		0			0
$40$	412.912	+	238.395i	1.63218	+	0.942338i
$41$	−105.357			−0.401315			−0.200658	−	0.979661i	$-0.564308\pi$
$41$	−105.357			−0.401315			−0.200658	+	0.979661i	$0.564308\pi$
$42$		0			0
$43$	−190.000			−0.673831			−0.336915	−	0.941535i	$-0.609384\pi$
$43$	−190.000			−0.673831			−0.336915	+	0.941535i	$0.609384\pi$
$44$		0			0
$45$		0			0
$46$	−110.000	−	190.526i	−0.352579	−	0.610684i
$47$	−21.0713	+	36.4966i	−0.0653950	+	0.113268i	−0.896869	−	0.442296i	$-0.854164\pi$
$47$	−21.0713	+	36.4966i	−0.0653950	+	0.113268i	0.831474	+	0.555563i	$0.187497\pi$
$48$		0			0
$49$		0			0
$50$		−	902.268i		−	2.55200i
$51$		0			0
$52$		0			0
$53$	309.860	−	178.898i	0.803068	−	0.463652i	−0.0414748	−	0.999140i	$-0.513206\pi$
$53$	309.860	−	178.898i	0.803068	−	0.463652i	0.844543	+	0.535488i	$0.179872\pi$
$54$		0			0
$55$		−	327.793i		−	0.803628i
$56$		0			0
$57$		0			0
$58$	178.000	−	308.305i	0.402975	−	0.697973i
$59$	−42.1426	−	72.9932i	−0.0929915	−	0.161066i	0.815777	−	0.578366i	$-0.196310\pi$
$59$	−42.1426	−	72.9932i	−0.0929915	−	0.161066i	−0.908769	+	0.417300i	$0.862976\pi$
$60$		0			0
$61$	−567.753	−	327.793i	−1.19169	−	0.688025i	−0.233004	−	0.972476i	$-0.574856\pi$
$61$	−567.753	−	327.793i	−1.19169	−	0.688025i	−0.958691	+	0.284450i	$0.908189\pi$
$62$	674.282			1.38119
$63$		0			0
$64$	−512.000			−1.00000
$65$	543.787	+	313.955i	1.03767	+	0.599098i
$66$		0			0
$67$	−148.000	−	256.344i	−0.269867	−	0.467423i	0.698960	−	0.715160i	$-0.253646\pi$
$67$	−148.000	−	256.344i	−0.269867	−	0.467423i	−0.968827	+	0.247737i	$0.920313\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	329.512i		−	0.550787i	−0.961332	−	0.275393i	$-0.911192\pi$
$71$		−	329.512i		−	0.550787i	0.961332	−	0.275393i	$-0.0888081\pi$
$72$		0			0
$73$	−696.788	+	402.291i	−1.11716	+	0.644994i	−0.940675	−	0.339308i	$-0.889807\pi$
$73$	−696.788	+	402.291i	−1.11716	+	0.644994i	−0.176488	+	0.984303i	$0.556474\pi$
$74$	450.706	−	260.215i	0.708021	−	0.408776i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−418.000	+	723.997i	−0.595300	+	1.03109i	0.398205	+	0.917297i	$0.369633\pi$
$79$	−418.000	+	723.997i	−0.595300	+	1.03109i	−0.993505	+	0.113793i	$0.963700\pi$
$80$	674.282	+	1167.89i	0.942338	+	1.63218i
$81$		0			0
$82$	−258.070	−	148.997i	−0.347549	−	0.200658i
$83$	−1222.14			−1.61623			−0.808113	−	0.589027i	$-0.799511\pi$
$83$	−1222.14			−1.61623			−0.808113	+	0.589027i	$0.799511\pi$
$84$		0			0
$85$	−1332.00			−1.69971
$86$	−465.403	−	268.701i	−0.583555	−	0.336915i
$87$		0			0
$88$	176.000	+	304.841i	0.213201	+	0.369274i
$89$	−347.677	+	602.193i	−0.414086	+	0.717218i	−0.995332	−	0.0965100i	$-0.969232\pi$
$89$	−347.677	+	602.193i	−0.414086	+	0.717218i	0.581246	+	0.813728i	$0.302565\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−103.228	+	59.5987i	−0.113268	+	0.0653950i
$95$	1631.36	−	941.866i	1.76183	−	1.01719i
$96$		0			0
$97$			566.187i			0.592656i	0.955086	+	0.296328i	$0.0957621\pi$
$97$			566.187i			0.592656i	−0.955086	+	0.296328i	$0.904238\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−368.748	−	638.690i	−0.363285	−	0.629228i	0.625214	−	0.780453i	$-0.285012\pi$
$101$	−368.748	−	638.690i	−0.363285	−	0.629228i	−0.988499	+	0.151225i	$0.951678\pi$
$102$		0			0
$103$	567.753	+	327.793i	0.543130	+	0.313576i	0.746347	−	0.665557i	$-0.231806\pi$
$103$	567.753	+	327.793i	0.543130	+	0.313576i	−0.203216	+	0.979134i	$0.565139\pi$
$104$	−674.282			−0.635757
$105$		0			0
$106$	1012.00			0.927303
$107$	1718.32	+	992.071i	1.55249	+	0.896328i	0.997939	+	0.0641758i	$0.0204418\pi$
$107$	1718.32	+	992.071i	1.55249	+	0.896328i	0.554547	+	0.832152i	$0.312891\pi$
$108$		0			0
$109$	422.000	+	730.925i	0.370828	+	0.642293i	0.989693	−	0.143204i	$-0.0457405\pi$
$109$	422.000	+	730.925i	0.370828	+	0.642293i	−0.618865	+	0.785497i	$0.712407\pi$
$110$	463.569	−	802.925i	0.401814	−	0.695962i
$111$		0			0
$112$		0			0
$113$		−	575.585i		−	0.479172i	−0.970875	−	0.239586i	$-0.922988\pi$
$113$		−	575.585i		−	0.479172i	0.970875	−	0.239586i	$-0.0770118\pi$
$114$		0			0
$115$	1419.38	−	819.482i	1.15094	−	0.664496i
$116$		0			0
$117$		0			0
$118$		−	238.395i		−	0.185983i
$119$		0			0
$120$		0			0
$121$	−544.500	+	943.102i	−0.409091	+	0.708566i
$122$	−927.138	−	1605.85i	−0.688025	−	1.19169i
$123$		0			0
$124$		0			0
$125$	4087.83			2.92502
$126$		0			0
$127$	−220.000			−0.153715			−0.0768577	−	0.997042i	$-0.524489\pi$
$127$	−220.000			−0.153715			−0.0768577	+	0.997042i	$0.524489\pi$
$128$	−1254.14	−	724.077i	−0.866025	−	0.500000i
$129$		0			0
$130$	888.000	+	1538.06i	0.599098	+	1.03767i
$131$	653.211	−	1131.39i	0.435659	−	0.754583i	−0.561691	−	0.827347i	$-0.689849\pi$
$131$	653.211	−	1131.39i	0.435659	−	0.754583i	0.997349	+	0.0727646i	$0.0231822\pi$
$132$		0			0
$133$		0			0
$134$		−	837.214i		−	0.539734i
$135$		0			0
$136$	1238.73	−	715.184i	0.781034	−	0.450930i
$137$	−1358.24	+	784.181i	−0.847025	+	0.489030i	−0.859646	−	0.510890i	$-0.829316\pi$
$137$	−1358.24	+	784.181i	−0.847025	+	0.489030i	0.0126208	+	0.999920i	$0.495983\pi$
$138$		0			0
$139$		−	655.585i		−	0.400043i	−0.979791	−	0.200022i	$-0.935899\pi$
$139$		−	655.585i		−	0.400043i	0.979791	−	0.200022i	$-0.0641012\pi$
$140$		0			0
$141$		0			0
$142$	466.000	−	807.136i	0.275393	−	0.476995i
$143$	231.784	+	401.462i	0.135544	+	0.234769i
$144$		0			0
$145$	2296.82	+	1326.07i	1.31545	+	0.759477i
$146$	−2275.70			−1.28999
$147$		0			0
$148$		0			0
$149$	1270.06	+	733.270i	0.698305	+	0.403166i	0.806716	−	0.590940i	$-0.201243\pi$
$149$	1270.06	+	733.270i	0.698305	+	0.403166i	−0.108411	+	0.994106i	$0.534576\pi$
$150$		0			0
$151$	−985.000	−	1706.07i	−0.530849	−	0.919457i	−0.999352	−	0.0359952i	$-0.988540\pi$
$151$	−985.000	−	1706.07i	−0.530849	−	0.919457i	0.468503	−	0.883462i	$-0.344793\pi$
$152$	−1011.42	+	1751.84i	−0.539719	+	0.934820i
$153$		0			0
$154$		0			0
$155$			5023.29i			2.60310i
$156$		0			0
$157$	−2271.01	+	1311.17i	−1.15444	+	0.666515i	−0.949965	−	0.312358i	$-0.898881\pi$
$157$	−2271.01	+	1311.17i	−1.15444	+	0.666515i	−0.204473	+	0.978872i	$0.565548\pi$
$158$	−2047.77	+	1182.28i	−1.03109	+	0.595300i
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	668.000	−	1157.01i	0.320993	−	0.555976i	−0.659700	−	0.751529i	$-0.729317\pi$
$163$	668.000	−	1157.01i	0.320993	−	0.555976i	0.980693	+	0.195553i	$0.0626502\pi$
$164$		0			0
$165$		0			0
$166$	−2993.61	−	1728.36i	−1.39969	−	0.808113i
$167$	−2317.84			−1.07401			−0.537006	−	0.843578i	$-0.680445\pi$
$167$	−2317.84			−1.07401			−0.537006	+	0.843578i	$0.680445\pi$
$168$		0			0
$169$	1309.00			0.595812
$170$	−3262.72	−	1883.73i	−1.47200	−	0.849857i
$171$		0			0
$172$		0			0
$173$	−115.892	+	200.731i	−0.0509313	+	0.0882157i	−0.890367	−	0.455243i	$-0.849552\pi$
$173$	−115.892	+	200.731i	−0.0509313	+	0.0882157i	0.839436	+	0.543459i	$0.182886\pi$
$174$		0			0
$175$		0			0
$176$			995.606i			0.426401i
$177$		0			0
$178$	−1703.26	+	983.378i	−0.717218	+	0.414086i
$179$	−94.3054	+	54.4472i	−0.0393783	+	0.0227351i	−0.519560	−	0.854434i	$-0.673904\pi$
$179$	−94.3054	+	54.4472i	−0.0393783	+	0.0227351i	0.480182	+	0.877169i	$0.340571\pi$
$180$		0			0
$181$			2592.54i			1.06465i	0.846539	+	0.532326i	$0.178682\pi$
$181$			2592.54i			1.06465i	−0.846539	+	0.532326i	$0.821318\pi$
$182$		0			0
$183$		0			0
$184$	−880.000	+	1524.20i	−0.352579	+	0.610684i
$185$	1938.56	+	3357.68i	0.770410	+	1.33439i
$186$		0			0
$187$	−851.630	−	491.689i	−0.333034	−	0.192277i
$188$		0			0
$189$		0			0
$190$	5328.00			2.03439
$191$	−1926.52	−	1112.28i	−0.729834	−	0.421370i	0.0885272	−	0.996074i	$-0.471784\pi$
$191$	−1926.52	−	1112.28i	−0.729834	−	0.421370i	−0.818362	+	0.574704i	$0.805117\pi$
$192$		0			0
$193$	−1870.00	−	3238.94i	−0.697438	−	1.20800i	−0.969352	−	0.245677i	$-0.920990\pi$
$193$	−1870.00	−	3238.94i	−0.697438	−	1.20800i	0.271914	−	0.962322i	$-0.412343\pi$
$194$	−800.710	+	1386.87i	−0.296328	+	0.513255i
$195$		0			0
$196$		0			0
$197$			1197.84i			0.433211i	0.976259	+	0.216605i	$0.0694985\pi$
$197$			1197.84i			0.433211i	−0.976259	+	0.216605i	$0.930502\pi$
$198$		0			0
$199$	696.788	−	402.291i	0.248211	−	0.143305i	−0.370734	−	0.928739i	$-0.620894\pi$
$199$	696.788	−	402.291i	0.248211	−	0.143305i	0.618945	+	0.785434i	$0.287560\pi$
$200$	−6251.10	+	3609.07i	−2.21010	+	1.27600i
$201$		0			0
$202$		−	2085.95i		−	0.726570i
$203$		0			0
$204$		0			0
$205$	1110.00	−	1922.58i	0.378174	−	0.655017i
$206$	927.138	+	1605.85i	0.313576	+	0.543130i
$207$		0			0
$208$	−1651.65	−	953.579i	−0.550582	−	0.317879i
$209$	1390.71			0.460274
$210$		0			0
$211$	3590.00			1.17131			0.585654	−	0.810561i	$-0.300838\pi$
$211$	3590.00			1.17131			0.585654	+	0.810561i	$0.300838\pi$
$212$		0			0
$213$		0			0
$214$	2806.00	+	4860.13i	0.896328	+	1.55249i
$215$	2001.77	−	3467.17i	0.634976	−	1.09981i
$216$		0			0
$217$		0			0
$218$			2387.19i			0.741656i
$219$		0			0
$220$		0			0
$221$	1631.36	−	941.866i	0.496548	−	0.286682i
$222$		0			0
$223$		−	3009.73i		−	0.903796i	−0.892070	−	0.451898i	$-0.850747\pi$
$223$		−	3009.73i		−	0.903796i	0.892070	−	0.451898i	$-0.149253\pi$
$224$		0			0
$225$		0			0
$226$	814.000	−	1409.89i	0.239586	−	0.414975i
$227$	−1854.28	−	3211.70i	−0.542170	−	0.939066i	−0.998779	−	0.0493984i	$-0.984270\pi$
$227$	−1854.28	−	3211.70i	−0.542170	−	0.939066i	0.456609	−	0.889667i	$-0.349064\pi$
$228$		0			0
$229$	−283.877	−	163.896i	−0.0819175	−	0.0472951i	0.458482	−	0.888704i	$-0.348393\pi$
$229$	−283.877	−	163.896i	−0.0819175	−	0.0472951i	−0.540399	+	0.841409i	$0.681727\pi$
$230$	4635.69			1.32899
$231$		0			0
$232$	−2848.00			−0.805950
$233$	557.259	+	321.734i	0.156683	+	0.0904612i	0.576292	−	0.817244i	$-0.304499\pi$
$233$	557.259	+	321.734i	0.156683	+	0.0904612i	−0.419608	+	0.907705i	$0.637833\pi$
$234$		0			0
$235$	−444.000	−	769.031i	−0.123248	−	0.213472i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			646.296i			0.174918i	0.996168	+	0.0874590i	$0.0278747\pi$
$239$			646.296i			0.174918i	−0.996168	+	0.0874590i	$0.972125\pi$
$240$		0			0
$241$	335.491	−	193.696i	0.0896716	−	0.0517719i	−0.454494	−	0.890750i	$-0.650180\pi$
$241$	335.491	−	193.696i	0.0896716	−	0.0517719i	0.544165	+	0.838978i	$0.316846\pi$
$242$	−2667.49	+	1540.08i	−0.708566	+	0.409091i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1332.00	+	2307.09i	−0.343130	+	0.594319i
$248$	−2697.13	−	4671.56i	−0.690596	−	1.19615i
$249$		0			0
$250$	10013.1	+	5781.07i	2.53314	+	1.46251i
$251$	−6194.96			−1.55786			−0.778930	−	0.627111i	$-0.784237\pi$
$251$	−6194.96			−1.55786			−0.778930	+	0.627111i	$0.784237\pi$
$252$		0			0
$253$	1210.00			0.300680
$254$	−538.888	−	311.127i	−0.133121	−	0.0768577i
$255$		0			0
$256$		0			0
$257$	−1780.53	+	3083.96i	−0.432164	+	0.748530i	−0.997059	−	0.0766326i	$-0.975583\pi$
$257$	−1780.53	+	3083.96i	−0.432164	+	0.748530i	0.564895	+	0.825162i	$0.308916\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	3200.06	−	1847.56i	0.754583	−	0.435659i
$263$	−520.517	+	300.520i	−0.122040	+	0.0704596i	−0.559777	−	0.828643i	$-0.689113\pi$
$263$	−520.517	+	300.520i	−0.122040	+	0.0704596i	0.437737	+	0.899103i	$0.355780\pi$
$264$		0			0
$265$			7539.23i			1.74767i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2433.74	−	4215.35i	−0.551626	−	0.955445i	−0.998157	−	0.0606768i	$-0.980674\pi$
$269$	−2433.74	−	4215.35i	−0.551626	−	0.955445i	0.446531	−	0.894768i	$-0.352659\pi$
$270$		0			0
$271$	−1548.42	−	893.980i	−0.347084	−	0.200389i	0.316316	−	0.948654i	$-0.397554\pi$
$271$	−1548.42	−	893.980i	−0.347084	−	0.200389i	−0.663400	+	0.748265i	$0.730887\pi$
$272$	4045.69			0.901860
$273$		0			0
$274$	−4436.00			−0.978060
$275$	4297.63	+	2481.24i	0.942388	+	0.544088i
$276$		0			0
$277$	563.000	+	975.145i	0.122121	+	0.211519i	0.920604	−	0.390498i	$-0.127697\pi$
$277$	563.000	+	975.145i	0.122121	+	0.211519i	−0.798483	+	0.602017i	$0.794364\pi$
$278$	927.138	−	1605.85i	0.200022	−	0.346448i
$279$		0			0
$280$		0			0
$281$			5075.61i			1.07753i	0.842456	+	0.538765i	$0.181109\pi$
$281$			5075.61i			1.07753i	−0.842456	+	0.538765i	$0.818891\pi$
$282$		0			0
$283$	6167.87	−	3561.02i	1.29555	−	0.747988i	0.315921	−	0.948786i	$-0.397687\pi$
$283$	6167.87	−	3561.02i	1.29555	−	0.747988i	0.979633	+	0.200797i	$0.0643533\pi$
$284$		0			0
$285$		0			0
$286$			1311.17i			0.271088i
$287$		0			0
$288$		0			0
$289$	458.500	−	794.145i	0.0933238	−	0.161642i
$290$	3750.69	+	6496.39i	0.759477	+	1.31545i
$291$		0			0
$292$		0			0
$293$	−231.784			−0.0462150			−0.0231075	−	0.999733i	$-0.507356\pi$
$293$	−231.784			−0.0462150			−0.0231075	+	0.999733i	$0.507356\pi$
$294$		0			0
$295$	1776.00			0.350518
$296$	−3605.65	−	2081.72i	−0.708021	−	0.408776i
$297$		0			0
$298$	2074.00	+	3592.27i	0.403166	+	0.698305i
$299$	−1158.92	+	2007.31i	−0.224154	+	0.388247i
$300$		0			0
$301$		0			0
$302$		−	5572.00i		−	1.06170i
$303$		0			0
$304$	−4954.94	+	2860.74i	−0.934820	+	0.539719i
$305$	11963.3	−	6907.02i	2.24596	−	1.29670i
$306$		0			0
$307$		−	8850.40i		−	1.64534i	−0.568520	−	0.822669i	$-0.692484\pi$
$307$		−	8850.40i		−	1.64534i	0.568520	−	0.822669i	$-0.307516\pi$
$308$		0			0
$309$		0			0
$310$	−7104.00	+	12304.5i	−1.30155	+	2.25435i
$311$	3244.98	+	5620.47i	0.591659	+	1.02478i	0.994009	+	0.109298i	$0.0348602\pi$
$311$	3244.98	+	5620.47i	0.591659	+	1.02478i	−0.402350	+	0.915486i	$0.631806\pi$
$312$		0			0
$313$	−9393.74	−	5423.48i	−1.69638	−	0.979403i	−0.949146	−	0.314837i	$-0.898050\pi$
$313$	−9393.74	−	5423.48i	−1.69638	−	0.979403i	−0.747230	−	0.664566i	$-0.768617\pi$
$314$	−7417.10			−1.33303
$315$		0			0
$316$		0			0
$317$	1541.95	+	890.247i	0.273201	+	0.157733i	0.630341	−	0.776318i	$-0.282915\pi$
$317$	1541.95	+	890.247i	0.273201	+	0.157733i	−0.357140	+	0.934051i	$0.616248\pi$
$318$		0			0
$319$	979.000	+	1695.68i	0.171829	+	0.297617i
$320$	5394.25	−	9343.12i	0.942338	−	1.63218i
$321$		0			0
$322$		0			0
$323$		−	5651.20i		−	0.973502i
$324$		0			0
$325$	−8232.43	+	4752.99i	−1.40509	+	0.811226i
$326$	3272.52	−	1889.39i	0.555976	−	0.320993i
$327$		0			0
$328$			2383.95i			0.401315i
$329$		0			0
$330$		0			0
$331$	4763.00	−	8249.76i	0.790931	−	1.36993i	−0.134460	−	0.990919i	$-0.542930\pi$
$331$	4763.00	−	8249.76i	0.790931	−	1.36993i	0.925391	−	0.379014i	$-0.123737\pi$
$332$		0			0
$333$		0			0
$334$	−5677.53	−	3277.93i	−0.930122	−	0.537006i
$335$	6237.11			1.01722
$336$		0			0
$337$	−8272.00			−1.33711			−0.668553	−	0.743665i	$-0.733086\pi$
$337$	−8272.00			−1.33711			−0.668553	+	0.743665i	$0.733086\pi$
$338$	3206.38	+	1851.21i	0.515989	+	0.297906i
$339$		0			0
$340$		0			0
$341$	−1854.28	+	3211.70i	−0.294471	+	0.510039i
$342$		0			0
$343$		0			0
$344$			4299.21i			0.673831i
$345$		0			0
$346$	−567.753	+	327.793i	−0.0882157	+	0.0509313i
$347$	8474.01	−	4892.47i	1.31098	−	0.756892i	0.328718	−	0.944428i	$-0.393383\pi$
$347$	8474.01	−	4892.47i	1.31098	−	0.756892i	0.982258	+	0.187536i	$0.0600500\pi$
$348$		0			0
$349$		−	6317.46i		−	0.968956i	−0.874803	−	0.484478i	$-0.839010\pi$
$349$		−	6317.46i		−	0.968956i	0.874803	−	0.484478i	$-0.160990\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2728.73	+	4726.31i	0.411433	+	0.712623i	0.995047	−	0.0994085i	$-0.0316951\pi$
$353$	2728.73	+	4726.31i	0.411433	+	0.712623i	−0.583614	+	0.812031i	$0.698362\pi$
$354$		0			0
$355$	6013.03	+	3471.62i	0.898981	+	0.519027i
$356$		0			0
$357$		0			0
$358$	−308.000			−0.0454701
$359$	9390.12	+	5421.39i	1.38048	+	0.797019i	0.992216	−	0.124530i	$-0.0397423\pi$
$359$	9390.12	+	5421.39i	1.38048	+	0.797019i	0.388262	+	0.921549i	$0.373076\pi$
$360$		0			0
$361$	566.500	+	981.207i	0.0825922	+	0.143054i
$362$	−3666.41	+	6350.40i	−0.532326	+	0.922016i
$363$		0			0
$364$		0			0
$365$		−	16953.6i		−	2.43121i
$366$		0			0
$367$	−3225.87	+	1862.46i	−0.458826	+	0.264903i	−0.711550	−	0.702635i	$-0.752007\pi$
$367$	−3225.87	+	1862.46i	−0.458826	+	0.264903i	0.252724	+	0.967538i	$0.418673\pi$
$368$	−4311.10	+	2489.02i	−0.610684	+	0.352579i
$369$		0			0
$370$			10966.2i			1.54082i
$371$		0			0
$372$		0			0
$373$	−2101.00	+	3639.04i	−0.291651	+	0.505154i	−0.974200	−	0.225686i	$-0.927538\pi$
$373$	−2101.00	+	3639.04i	−0.291651	+	0.505154i	0.682550	+	0.730839i	$0.260871\pi$
$374$	−1390.71	−	2408.77i	−0.192277	−	0.333034i
$375$		0			0
$376$	825.823	+	476.789i	0.113268	+	0.0653950i
$377$	−3750.69			−0.512389
$378$		0			0
$379$	−2506.00			−0.339643			−0.169821	−	0.985475i	$-0.554319\pi$
$379$	−2506.00			−0.339643			−0.169821	+	0.985475i	$0.554319\pi$
$380$		0			0
$381$		0			0
$382$	−3146.00	−	5449.03i	−0.421370	−	0.729834i
$383$	−6553.18	+	11350.4i	−0.874286	+	1.51431i	−0.0167654	+	0.999859i	$0.505337\pi$
$383$	−6553.18	+	11350.4i	−0.874286	+	1.51431i	−0.857521	+	0.514449i	$0.827996\pi$
$384$		0			0
$385$		0			0
$386$		−	10578.3i		−	1.39488i
$387$		0			0
$388$		0			0
$389$	−4011.04	+	2315.77i	−0.522796	+	0.301837i	−0.738078	−	0.674715i	$-0.764266\pi$
$389$	−4011.04	+	2315.77i	−0.522796	+	0.301837i	0.215282	+	0.976552i	$0.430933\pi$
$390$		0			0
$391$		−	4916.89i		−	0.635953i
$392$		0			0
$393$		0			0
$394$	−1694.00	+	2934.09i	−0.216605	+	0.375171i
$395$	−8807.81	−	15255.6i	−1.12195	−	1.94327i
$396$		0			0
$397$	6967.88	+	4022.91i	0.880877	+	0.508574i	0.870947	−	0.491376i	$-0.163506\pi$
$397$	6967.88	+	4022.91i	0.880877	+	0.508574i	0.00992932	+	0.999951i	$0.496839\pi$
$398$	2275.70			0.286610
$399$		0			0
$400$	−20416.0			−2.55200
$401$	−11736.7	−	6776.20i	−1.46161	−	0.843859i	−0.462521	−	0.886608i	$-0.653055\pi$
$401$	−11736.7	−	6776.20i	−1.46161	−	0.843859i	−0.999086	+	0.0427492i	$0.986388\pi$
$402$		0			0
$403$	−3552.00	−	6152.24i	−0.439051	−	0.760459i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			2862.37i			0.348605i
$408$		0			0
$409$	8800.18	−	5080.79i	1.06391	−	0.614251i	0.137402	−	0.990515i	$-0.456125\pi$
$409$	8800.18	−	5080.79i	1.06391	−	0.614251i	0.926512	+	0.376264i	$0.122792\pi$
$410$	5437.87	−	3139.55i	0.655017	−	0.378174i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	12876.0	−	22301.9i	1.52303	−	2.63797i
$416$		0			0
$417$		0			0
$418$	3406.52	+	1966.76i	0.398609	+	0.230137i
$419$	8934.23			1.04168			0.520842	−	0.853653i	$-0.325618\pi$
$419$	8934.23			1.04168			0.520842	+	0.853653i	$0.325618\pi$
$420$		0			0
$421$	5606.00			0.648978			0.324489	−	0.945889i	$-0.394808\pi$
$421$	5606.00			0.648978			0.324489	+	0.945889i	$0.394808\pi$
$422$	8793.67	+	5077.03i	1.01438	+	0.585654i
$423$		0			0
$424$	−4048.00	−	7011.34i	−0.463652	−	0.803068i
$425$	10082.6	−	17463.6i	1.15077	−	1.99320i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$	9806.65	−	5661.87i	1.09981	−	0.634976i
$431$	765.466	−	441.942i	0.0855480	−	0.0493911i	−0.456616	−	0.889664i	$-0.650939\pi$
$431$	765.466	−	441.942i	0.0855480	−	0.0493911i	0.542164	+	0.840273i	$0.317605\pi$
$432$		0			0
$433$			1966.76i			0.218282i	0.994026	+	0.109141i	$0.0348101\pi$
$433$			1966.76i			0.218282i	−0.994026	+	0.109141i	$0.965190\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3476.77	+	6021.93i	0.380586	+	0.659195i
$438$		0			0
$439$	−335.491	−	193.696i	−0.0364740	−	0.0210583i	0.481652	−	0.876363i	$-0.340037\pi$
$439$	−335.491	−	193.696i	−0.0364740	−	0.0210583i	−0.518126	+	0.855304i	$0.673370\pi$
$440$	−7417.10			−0.803628
$441$		0			0
$442$	5328.00			0.573365
$443$	−2271.90	−	1311.68i	−0.243660	−	0.140677i	0.373198	−	0.927752i	$-0.378261\pi$
$443$	−2271.90	−	1311.68i	−0.243660	−	0.140677i	−0.616858	+	0.787075i	$0.711595\pi$
$444$		0			0
$445$	−7326.00	−	12689.0i	−0.780417	−	1.35172i
$446$	4256.40	−	7372.31i	0.451898	−	0.782711i
$447$		0			0
$448$		0			0
$449$		−	5140.67i		−	0.540319i	−0.962816	−	0.270159i	$-0.912924\pi$
$449$		−	5140.67i		−	0.540319i	0.962816	−	0.270159i	$-0.0870764\pi$
$450$		0			0
$451$	1419.38	−	819.482i	0.148195	−	0.0855607i
$452$		0			0
$453$		0			0
$454$		−	10489.4i		−	1.08434i
$455$		0			0
$456$		0			0
$457$	−1804.00	+	3124.62i	−0.184655	+	0.319833i	−0.943460	−	0.331485i	$-0.892450\pi$
$457$	−1804.00	+	3124.62i	−0.184655	+	0.319833i	0.758805	+	0.651318i	$0.225784\pi$
$458$	−463.569	−	802.925i	−0.0472951	−	0.0819175i
$459$		0			0
$460$		0			0
$461$	−1538.21			−0.155404			−0.0777021	−	0.996977i	$-0.524758\pi$
$461$	−1538.21			−0.155404			−0.0777021	+	0.996977i	$0.524758\pi$
$462$		0			0
$463$	1772.00			0.177866			0.0889329	−	0.996038i	$-0.471654\pi$
$463$	1772.00			0.177866			0.0889329	+	0.996038i	$0.471654\pi$
$464$	−6976.15	−	4027.68i	−0.697973	−	0.402975i
$465$		0			0
$466$	910.000	+	1576.17i	0.0904612	+	0.156683i
$467$	6384.61	−	11058.5i	0.632643	−	1.09577i	−0.354366	−	0.935107i	$-0.615303\pi$
$467$	6384.61	−	11058.5i	0.632643	−	1.09577i	0.987009	−	0.160663i	$-0.0513633\pi$
$468$		0			0
$469$		0			0
$470$		−	2511.64i		−	0.246497i
$471$		0			0
$472$	−1651.65	+	953.579i	−0.161066	+	0.0929915i
$473$	2559.72	−	1477.85i	0.248829	−	0.143661i
$474$		0			0
$475$			28518.0i			2.75472i
$476$		0			0
$477$		0			0
$478$	−914.000	+	1583.09i	−0.0874590	+	0.151483i
$479$	2317.84	+	4014.62i	0.221096	+	0.382950i	0.955141	−	0.296151i	$-0.0957033\pi$
$479$	2317.84	+	4014.62i	0.221096	+	0.382950i	−0.734045	+	0.679101i	$0.762370\pi$
$480$		0			0
$481$	−4748.48	−	2741.54i	−0.450129	−	0.259882i
$482$	1095.71			0.103544
$483$		0			0
$484$		0			0
$485$	−10331.9	−	5965.15i	−0.967319	−	0.558482i
$486$		0			0
$487$	−979.000	−	1695.68i	−0.0910939	−	0.157779i	0.816878	−	0.576811i	$-0.195703\pi$
$487$	−979.000	−	1695.68i	−0.0910939	−	0.157779i	−0.907972	+	0.419032i	$0.862370\pi$
$488$	−7417.10	+	12846.8i	−0.688025	+	1.19169i
$489$		0			0
$490$		0			0
$491$		−	7126.22i		−	0.654994i	−0.944852	−	0.327497i	$-0.893795\pi$
$491$		−	7126.22i		−	0.654994i	0.944852	−	0.327497i	$-0.106205\pi$
$492$		0			0
$493$	6890.46	−	3978.21i	0.629474	−	0.363427i
$494$	−6525.44	+	3767.46i	−0.594319	+	0.343130i
$495$		0			0
$496$		−	15257.3i		−	1.38119i
$497$		0			0
$498$		0			0
$499$	−5155.00	+	8928.72i	−0.462464	+	0.801011i	−0.999083	−	0.0428136i	$-0.986368\pi$
$499$	−5155.00	+	8928.72i	−0.462464	+	0.801011i	0.536619	+	0.843825i	$0.319701\pi$
$500$		0			0
$501$		0			0
$502$	−15174.5	−	8761.00i	−1.34915	−	0.778930i
$503$	−126.428			−0.0112070			−0.00560352	−	0.999984i	$-0.501784\pi$
$503$	−126.428			−0.0112070			−0.00560352	+	0.999984i	$0.501784\pi$
$504$		0			0
$505$	15540.0			1.36935
$506$	2963.88	+	1711.20i	0.260397	+	0.150340i
$507$		0			0
$508$		0			0
$509$	−3550.52	+	6149.67i	−0.309182	+	0.535520i	−0.978184	−	0.207742i	$-0.933389\pi$
$509$	−3550.52	+	6149.67i	−0.309182	+	0.535520i	0.669001	+	0.743261i	$0.266722\pi$
$510$		0			0
$511$		0			0
$512$			11585.2i			1.00000i
$513$		0			0
$514$	−8722.76	+	5036.09i	−0.748530	+	0.432164i
$515$	−11963.3	+	6907.02i	−1.02362	+	0.590990i
$516$		0			0
$517$		−	655.585i		−	0.0557691i
$518$		0			0
$519$		0			0
$520$	7104.00	−	12304.5i	0.599098	−	1.03767i
$521$	2244.09	+	3886.89i	0.188705	+	0.326847i	0.944819	−	0.327593i	$-0.106238\pi$
$521$	2244.09	+	3886.89i	0.188705	+	0.326847i	−0.756113	+	0.654441i	$0.772904\pi$
$522$		0			0
$523$	8051.78	+	4648.70i	0.673192	+	0.388668i	0.797285	−	0.603603i	$-0.206269\pi$
$523$	8051.78	+	4648.70i	0.673192	+	0.388668i	−0.124093	+	0.992271i	$0.539602\pi$
$524$		0			0
$525$		0			0
$526$	−1700.00			−0.140919
$527$	13050.9	+	7534.93i	1.07876	+	0.622821i
$528$		0			0
$529$	−3058.50	−	5297.48i	−0.251377	−	0.435397i
$530$	−10662.1	+	18467.3i	−0.873833	+	1.51352i
$531$		0			0
$532$		0			0
$533$			3139.55i			0.255139i
$534$		0			0
$535$	−36207.2	+	20904.2i	−2.92593	+	1.68929i
$536$	−5800.39	+	3348.86i	−0.467423	+	0.269867i
$537$		0			0
$538$		−	13767.3i		−	1.10325i
$539$		0			0
$540$		0			0
$541$	7823.00	−	13549.8i	0.621695	−	1.07681i	−0.367475	−	0.930033i	$-0.619778\pi$
$541$	7823.00	−	13549.8i	0.621695	−	1.07681i	0.989170	−	0.146774i	$-0.0468890\pi$
$542$	−2528.56	−	4379.59i	−0.200389	−	0.347084i
$543$		0			0
$544$		0			0
$545$	−17784.2			−1.39778
$546$		0			0
$547$	1880.00			0.146952			0.0734762	−	0.997297i	$-0.476591\pi$
$547$	1880.00			0.146952			0.0734762	+	0.997297i	$0.476591\pi$
$548$		0			0
$549$		0			0
$550$	7018.00	+	12155.5i	0.544088	+	0.942388i
$551$	−5626.04	+	9744.59i	−0.434986	+	0.753418i
$552$		0			0
$553$		0			0
$554$			3184.81i			0.244241i
$555$		0			0
$556$		0			0
$557$	6063.71	−	3500.89i	0.461271	−	0.266315i	−0.251308	−	0.967907i	$-0.580861\pi$
$557$	6063.71	−	3500.89i	0.461271	−	0.266315i	0.712578	+	0.701593i	$0.247527\pi$
$558$		0			0
$559$			5661.87i			0.428393i
$560$		0			0
$561$		0			0
$562$	−7178.00	+	12432.7i	−0.538765	+	0.933168i
$563$	4193.19	+	7262.82i	0.313893	+	0.543679i	0.979202	−	0.202890i	$-0.0650333\pi$
$563$	4193.19	+	7262.82i	0.313893	+	0.543679i	−0.665308	+	0.746569i	$0.731700\pi$
$564$		0			0
$565$	10503.4	+	6064.16i	0.782094	+	0.451542i
$566$	20144.2			1.49598
$567$		0			0
$568$	−7456.00			−0.550787
$569$	−15506.5	−	8952.68i	−1.14247	−	0.659606i	−0.195430	−	0.980718i	$-0.562610\pi$
$569$	−15506.5	−	8952.68i	−1.14247	−	0.659606i	−0.947041	+	0.321112i	$0.895944\pi$
$570$		0			0
$571$	12368.0	+	21422.0i	0.906453	+	1.57002i	0.818955	+	0.573858i	$0.194554\pi$
$571$	12368.0	+	21422.0i	0.906453	+	1.57002i	0.0874983	+	0.996165i	$0.472113\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			24812.4i			1.79956i
$576$		0			0
$577$	15019.7	−	8671.60i	1.08367	−	0.625656i	0.151785	−	0.988414i	$-0.451498\pi$
$577$	15019.7	−	8671.60i	1.08367	−	0.625656i	0.931884	+	0.362757i	$0.118165\pi$
$578$	2246.18	−	1296.83i	0.161642	−	0.0933238i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−2783.00	+	4820.30i	−0.197702	+	0.342429i
$584$	9102.80	+	15766.5i	0.644994	+	1.11716i
$585$		0			0
$586$	−567.753	−	327.793i	−0.0400233	−	0.0231075i
$587$	3329.27			0.234095			0.117047	−	0.993126i	$-0.462657\pi$
$587$	3329.27			0.234095			0.117047	+	0.993126i	$0.462657\pi$
$588$		0			0
$589$	−21312.0			−1.49091
$590$	4350.29	+	2511.64i	0.303557	+	0.175259i
$591$		0			0
$592$	−5888.00	−	10198.3i	−0.408776	−	0.708021i
$593$	11283.7	−	19543.9i	0.781392	−	1.35341i	−0.149739	−	0.988726i	$-0.547843\pi$
$593$	11283.7	−	19543.9i	0.781392	−	1.35341i	0.931131	−	0.364685i	$-0.118823\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−5677.53	+	3277.93i	−0.388247	+	0.224154i
$599$	−21838.4	+	12608.4i	−1.48964	+	0.860044i	−0.999930	−	0.0118422i	$-0.996230\pi$
$599$	−21838.4	+	12608.4i	−1.48964	+	0.860044i	−0.489709	+	0.871886i	$0.662897\pi$
$600$		0			0
$601$		−	13290.5i		−	0.902048i	−0.892512	−	0.451024i	$-0.851059\pi$
$601$		−	13290.5i		−	0.902048i	0.892512	−	0.451024i	$-0.148941\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−11473.3	−	19872.4i	−0.771003	−	1.33542i
$606$		0			0
$607$	−15922.9	−	9193.09i	−1.06473	−	0.614722i	−0.137993	−	0.990433i	$-0.544065\pi$
$607$	−15922.9	−	9193.09i	−1.06473	−	0.614722i	−0.926737	+	0.375711i	$0.877398\pi$
$608$		0			0
$609$		0			0
$610$	39072.0			2.59341
$611$	1087.57	+	627.911i	0.0720107	+	0.0415754i
$612$		0			0
$613$	13277.0	+	22996.4i	0.874801	+	1.51520i	0.856975	+	0.515359i	$0.172341\pi$
$613$	13277.0	+	22996.4i	0.874801	+	1.51520i	0.0178263	+	0.999841i	$0.494325\pi$
$614$	12516.4	−	21679.0i	0.822669	−	1.42491i
$615$		0			0
$616$		0			0
$617$			26475.5i			1.72749i	0.503927	+	0.863746i	$0.331888\pi$
$617$			26475.5i			1.72749i	−0.503927	+	0.863746i	$0.668112\pi$
$618$		0			0
$619$	14193.8	−	8194.82i	0.921645	−	0.532112i	0.0374857	−	0.999297i	$-0.488065\pi$
$619$	14193.8	−	8194.82i	0.921645	−	0.532112i	0.884160	+	0.467185i	$0.154732\pi$
$620$		0			0
$621$		0			0
$622$			18356.4i			1.18332i
$623$		0			0
$624$		0			0
$625$	−23130.5	+	40063.2i	−1.48035	+	2.56404i
$626$	−15339.9	−	26569.5i	−0.979403	−	1.69638i
$627$		0			0
$628$		0			0
$629$	11631.4			0.737318
$630$		0			0
$631$	24860.0			1.56840			0.784200	−	0.620508i	$-0.213073\pi$
$631$	24860.0			1.56840			0.784200	+	0.620508i	$0.213073\pi$
$632$	16382.2	+	9458.26i	1.03109	+	0.595300i
$633$		0			0
$634$	2518.00	+	4361.30i	0.157733	+	0.273201i
$635$	2317.84	−	4014.62i	0.144852	−	0.250890i
$636$		0			0
$637$		0			0
$638$			5538.06i			0.343658i
$639$		0			0
$640$	26426.3	−	15257.3i	1.63218	−	0.942338i
$641$	4571.97	−	2639.63i	0.281719	−	0.162651i	−0.352482	−	0.935819i	$-0.614662\pi$
$641$	4571.97	−	2639.63i	0.281719	−	0.162651i	0.634201	+	0.773168i	$0.281329\pi$
$642$		0			0
$643$			2652.14i			0.162660i	0.996687	+	0.0813299i	$0.0259167\pi$
$643$			2652.14i			0.162660i	−0.996687	+	0.0813299i	$0.974083\pi$
$644$		0			0
$645$		0			0
$646$	7992.00	−	13842.6i	0.486751	−	0.843077i
$647$	11504.9	+	19927.1i	0.699081	+	1.21084i	0.968785	+	0.247901i	$0.0797408\pi$
$647$	11504.9	+	19927.1i	0.699081	+	1.21084i	−0.269704	+	0.962943i	$0.586926\pi$
$648$		0			0
$649$	1135.51	+	655.585i	0.0686788	+	0.0396517i
$650$	−26887.0			−1.62245
$651$		0			0
$652$		0			0
$653$	−5079.02	−	2932.37i	−0.304376	−	0.175731i	0.340031	−	0.940414i	$-0.389562\pi$
$653$	−5079.02	−	2932.37i	−0.304376	−	0.175731i	−0.644407	+	0.764683i	$0.722896\pi$
$654$		0			0
$655$	13764.0	+	23839.9i	0.821075	+	1.42214i
$656$	−3371.41	+	5839.45i	−0.200658	+	0.347549i
$657$		0			0
$658$		0			0
$659$			2759.13i			0.163096i	0.996669	+	0.0815482i	$0.0259864\pi$
$659$			2759.13i			0.163096i	−0.996669	+	0.0815482i	$0.974014\pi$
$660$		0			0
$661$	18168.1	−	10489.4i	1.06907	−	0.617230i	0.141145	−	0.989989i	$-0.454922\pi$
$661$	18168.1	−	10489.4i	1.06907	−	0.617230i	0.927928	+	0.372759i	$0.121588\pi$
$662$	23333.8	−	13471.8i	1.36993	−	0.790931i
$663$		0			0
$664$			27653.8i			1.61623i
$665$		0			0
$666$		0			0
$667$	−4895.00	+	8478.39i	−0.284161	+	0.492181i
$668$		0			0
$669$		0			0
$670$	15277.7	+	8820.60i	0.880941	+	0.508611i
$671$	10198.5			0.586750
$672$		0			0
$673$	−13636.0			−0.781024			−0.390512	−	0.920598i	$-0.627702\pi$
$673$	−13636.0			−0.781024			−0.390512	+	0.920598i	$0.627702\pi$
$674$	−20262.2	−	11698.4i	−1.15797	−	0.668553i
$675$		0			0
$676$		0			0
$677$	−4983.36	+	8631.44i	−0.282904	+	0.490005i	−0.972099	−	0.234572i	$-0.924631\pi$
$677$	−4983.36	+	8631.44i	−0.282904	+	0.490005i	0.689194	+	0.724576i	$0.257965\pi$
$678$		0			0
$679$		0			0
$680$			30139.7i			1.69971i
$681$		0			0
$682$	−9084.06	+	5244.68i	−0.510039	+	0.294471i
$683$	−175.139	+	101.116i	−0.00981184	+	0.00566487i	−0.504898	−	0.863179i	$-0.668470\pi$
$683$	−175.139	+	101.116i	−0.00981184	+	0.00566487i	0.495086	+	0.868844i	$0.335137\pi$
$684$		0			0
$685$		−	33047.5i		−	1.84333i
$686$		0			0
$687$		0			0
$688$	−6080.00	+	10530.9i	−0.336915	+	0.583555i
$689$	−5331.04	−	9233.63i	−0.294770	−	0.510556i
$690$		0			0
$691$	17393.9	+	10042.4i	0.957591	+	0.552865i	0.895431	−	0.445201i	$-0.146868\pi$
$691$	17393.9	+	10042.4i	0.957591	+	0.552865i	0.0621600	+	0.998066i	$0.480201\pi$
$692$		0			0
$693$		0			0
$694$	27676.0			1.51378
$695$	11963.3	+	6907.02i	0.652941	+	0.376976i
$696$		0			0
$697$	−3330.00	−	5767.73i	−0.180965	−	0.313441i
$698$	8934.23	−	15474.5i	0.484478	−	0.839141i
$699$		0			0
$700$		0			0
$701$		−	22883.4i		−	1.23294i	−0.787377	−	0.616472i	$-0.788561\pi$
$701$		−	22883.4i		−	1.23294i	0.787377	−	0.616472i	$-0.211439\pi$
$702$		0			0
$703$	−14245.5	+	8224.61i	−0.764264	+	0.441248i
$704$	6897.76	−	3982.43i	0.369274	−	0.213201i
$705$		0			0
$706$			15436.1i			0.822866i
$707$		0			0
$708$		0			0
$709$	−6106.00	+	10575.9i	−0.323435	+	0.560206i	−0.981194	−	0.193022i	$-0.938171\pi$
$709$	−6106.00	+	10575.9i	−0.323435	+	0.560206i	0.657759	+	0.753228i	$0.271504\pi$
$710$	9819.23	+	17007.4i	0.519027	+	0.898981i
$711$		0			0
$712$	13626.1	+	7867.02i	0.717218	+	0.414086i
$713$	−18542.8			−0.973957
$714$		0			0
$715$	−9768.00			−0.510913
$716$		0			0
$717$		0			0
$718$	15334.0	+	26559.3i	0.797019	+	1.38048i
$719$	−14412.8	+	24963.7i	−0.747574	+	1.29484i	0.201408	+	0.979507i	$0.435448\pi$
$719$	−14412.8	+	24963.7i	−0.747574	+	1.29484i	−0.948982	+	0.315329i	$0.897885\pi$
$720$		0			0
$721$		0			0
$722$			3204.61i			0.165184i
$723$		0			0
$724$		0			0
$725$	−34771.7	+	20075.5i	−1.78123	+	1.02839i
$726$		0			0
$727$		−	3277.93i		−	0.167224i	−0.996498	−	0.0836118i	$-0.973354\pi$
$727$		−	3277.93i		−	0.167224i	0.996498	−	0.0836118i	$-0.0266456\pi$
$728$		0			0
$729$		0			0
$730$	23976.0	−	41527.7i	1.21560	−	2.10549i
$731$	−6005.32	−	10401.5i	−0.303851	−	0.526285i
$732$		0			0
$733$	−10503.4	−	6064.16i	−0.529268	−	0.305573i	0.211450	−	0.977389i	$-0.432181\pi$
$733$	−10503.4	−	6064.16i	−0.529268	−	0.305573i	−0.740718	+	0.671816i	$0.765515\pi$
$734$	−10535.7			−0.529807
$735$		0			0
$736$		0			0
$737$	3987.77	+	2302.34i	0.199310	+	0.115072i
$738$		0			0
$739$	−880.000	−	1524.20i	−0.0438042	−	0.0758711i	0.843292	−	0.537456i	$-0.180614\pi$
$739$	−880.000	−	1524.20i	−0.0438042	−	0.0758711i	−0.887096	+	0.461584i	$0.847281\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			22436.5i			1.10783i	0.832574	+	0.553913i	$0.186866\pi$
$743$			22436.5i			1.10783i	−0.832574	+	0.553913i	$0.813134\pi$
$744$		0			0
$745$	−26761.8	+	15451.0i	−1.31608	+	0.759838i
$746$	−10292.8	+	5942.53i	−0.505154	+	0.291651i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	2561.00	−	4435.78i	0.124437	−	0.215531i	−0.797076	−	0.603879i	$-0.793621\pi$
$751$	2561.00	−	4435.78i	0.124437	−	0.215531i	0.921513	+	0.388348i	$0.126954\pi$
$752$	1348.56	+	2335.78i	0.0653950	+	0.113268i
$753$		0			0
$754$	−9187.28	−	5304.28i	−0.443742	−	0.256194i
$755$	41510.5			2.00095
$756$		0			0
$757$	−18772.0			−0.901295			−0.450647	−	0.892702i	$-0.648807\pi$
$757$	−18772.0			−0.901295			−0.450647	+	0.892702i	$0.648807\pi$
$758$	−6138.42	−	3544.02i	−0.294139	−	0.169821i
$759$		0			0
$760$	−21312.0	−	36913.5i	−1.01719	−	1.76183i
$761$	−14486.5	+	25091.4i	−0.690061	+	1.19522i	0.281757	+	0.959486i	$0.409083\pi$
$761$	−14486.5	+	25091.4i	−0.690061	+	1.19522i	−0.971818	+	0.235734i	$0.924251\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−32103.9	+	18535.2i	−1.51431	+	0.874286i
$767$	−2175.15	+	1255.82i	−0.102399	+	0.0591201i
$768$		0			0
$769$		−	11740.9i		−	0.550571i	−0.961363	−	0.275285i	$-0.911228\pi$
$769$		−	11740.9i		−	0.550571i	0.961363	−	0.275285i	$-0.0887724\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6353.00	−	11003.7i	−0.295603	−	0.512000i	0.679522	−	0.733655i	$-0.262187\pi$
$773$	−6353.00	−	11003.7i	−0.295603	−	0.512000i	−0.975125	+	0.221655i	$0.928854\pi$
$774$		0			0
$775$	−65859.4	−	38023.9i	−3.05257	−	1.76240i
$776$	12811.4			0.592656
$777$		0			0
$778$	−13100.0			−0.603673
$779$	8156.80	+	4709.33i	0.375158	+	0.216597i
$780$		0			0
$781$	2563.00	+	4439.25i	0.117428	+	0.203391i
$782$	6953.53	−	12043.9i	0.317977	−	0.550752i
$783$		0			0
$784$		0			0
$785$		−	55256.2i		−	2.51233i
$786$		0			0
$787$	22813.4	−	13171.3i	1.03330	−	0.596577i	0.115373	−	0.993322i	$-0.463194\pi$
$787$	22813.4	−	13171.3i	1.03330	−	0.596577i	0.917929	+	0.396745i	$0.129860\pi$
$788$		0			0
$789$		0			0
$790$		−	49824.5i		−	2.24389i
$791$		0			0
$792$		0			0
$793$	−9768.00	+	16918.7i	−0.437417	+	0.757629i
$794$	11378.5	+	19708.2i	0.508574	+	0.880877i
$795$		0			0
$796$		0			0
$797$	−19448.8			−0.864382			−0.432191	−	0.901782i	$-0.642259\pi$
$797$	−19448.8			−0.864382			−0.432191	+	0.901782i	$0.642259\pi$
$798$		0			0
$799$	−2664.00			−0.117954
$800$		0			0
$801$		0			0
$802$	−19166.0	−	33196.5i	−0.843859	−	1.46161i
$803$	6258.18	−	10839.5i	0.275027	−	0.476360i
$804$		0			0
$805$		0			0
$806$		−	20093.1i		−	0.878103i
$807$		0			0
$808$	−14451.9	+	8343.81i	−0.629228	+	0.363285i
$809$	−29958.5	+	17296.5i	−1.30196	+	0.751686i	−0.980740	−	0.195319i	$-0.937426\pi$
$809$	−29958.5	+	17296.5i	−1.30196	+	0.751686i	−0.321219	+	0.947005i	$0.604092\pi$
$810$		0			0
$811$			28607.4i			1.23864i	0.785137	+	0.619322i	$0.212592\pi$
$811$			28607.4i			1.23864i	−0.785137	+	0.619322i	$0.787408\pi$
$812$		0			0
$813$		0			0
$814$	−4048.00	+	7011.34i	−0.174303	+	0.301901i
$815$	14075.6	+	24379.7i	0.604967	+	1.04783i
$816$		0			0
$817$	14710.0	+	8492.81i	0.629911	+	0.363679i
$818$	28741.3			1.22850
$819$		0			0
$820$		0			0
$821$	−24655.3	−	14234.8i	−1.04808	−	0.605112i	−0.125972	−	0.992034i	$-0.540205\pi$
$821$	−24655.3	−	14234.8i	−1.04808	−	0.605112i	−0.922112	+	0.386922i	$0.873538\pi$
$822$		0			0
$823$	−11734.0	−	20323.9i	−0.496988	−	0.860809i	0.503005	−	0.864283i	$-0.332228\pi$
$823$	−11734.0	−	20323.9i	−0.496988	−	0.860809i	−0.999994	+	0.00347391i	$0.998894\pi$
$824$	7417.10	−	12846.8i	0.313576	−	0.543130i
$825$		0			0
$826$		0			0
$827$			37447.0i			1.57456i	0.616598	+	0.787278i	$0.288511\pi$
$827$			37447.0i			1.57456i	−0.616598	+	0.787278i	$0.711489\pi$
$828$		0			0
$829$	−9367.93	+	5408.58i	−0.392475	+	0.226596i	−0.683232	−	0.730201i	$-0.739426\pi$
$829$	−9367.93	+	5408.58i	−0.392475	+	0.226596i	0.290757	+	0.956797i	$0.406093\pi$
$830$	63079.3	−	36418.8i	2.63797	−	1.52303i
$831$		0			0
$832$			15257.3i			0.635757i
$833$		0			0
$834$		0			0
$835$	24420.0	−	42296.7i	1.01208	−	1.75298i
$836$		0			0
$837$		0			0
$838$	21884.3	+	12634.9i	0.902125	+	0.520842i
$839$	−42690.5			−1.75666			−0.878331	−	0.478054i	$-0.841342\pi$
$839$	−42690.5			−1.75666			−0.878331	+	0.478054i	$0.841342\pi$
$840$		0			0
$841$	8547.00			0.350445
$842$	13731.8	+	7928.08i	0.562031	+	0.324489i
$843$		0			0
$844$		0			0
$845$	−13791.2	+	23887.0i	−0.561456	+	0.972471i
$846$		0			0
$847$		0			0
$848$		−	22898.9i		−	0.927303i
$849$		0			0
$850$	49394.6	−	28518.0i	1.99320	−	1.15077i
$851$	−12394.4	+	7155.92i	−0.499266	+	0.288251i
$852$		0			0
$853$			4589.10i			0.184206i	0.995749	+	0.0921030i	$0.0293589\pi$
$853$			4589.10i			0.184206i	−0.995749	+	0.0921030i	$0.970641\pi$
$854$		0			0
$855$		0			0
$856$	22448.0	−	38881.1i	0.896328	−	1.55249i
$857$	−2391.59	−	4142.36i	−0.0953270	−	0.165111i	0.814418	−	0.580279i	$-0.197056\pi$
$857$	−2391.59	−	4142.36i	−0.0953270	−	0.165111i	−0.909745	+	0.415167i	$0.863723\pi$
$858$		0			0
$859$	32078.1	+	18520.3i	1.27414	+	0.735627i	0.975765	−	0.218820i	$-0.0702208\pi$
$859$	32078.1	+	18520.3i	1.27414	+	0.735627i	0.298379	+	0.954448i	$0.403554\pi$
$860$		0			0
$861$		0			0
$862$	2500.00			0.0987823
$863$	1034.91	+	597.505i	0.0408212	+	0.0235682i	0.520272	−	0.854001i	$-0.325831\pi$
$863$	1034.91	+	597.505i	0.0408212	+	0.0235682i	−0.479450	+	0.877569i	$0.659164\pi$
$864$		0			0
$865$	−2442.00	−	4229.67i	−0.0959890	−	0.166258i
$866$	−2781.41	+	4817.55i	−0.109141	+	0.189038i
$867$		0			0
$868$		0			0
$869$		−	13005.1i		−	0.507673i
$870$		0			0
$871$	−7638.86	+	4410.30i	−0.297168	+	0.171570i
$872$	16539.0	−	9548.77i	0.642293	−	0.370828i
$873$		0			0
$874$			19667.6i			0.761173i
$875$		0			0
$876$		0			0
$877$	−17149.0	+	29702.9i	−0.660297	+	1.14367i	0.320240	+	0.947336i	$0.396236\pi$
$877$	−17149.0	+	29702.9i	−0.660297	+	1.14367i	−0.980538	+	0.196332i	$0.937097\pi$
$878$	−547.854	−	948.911i	−0.0210583	−	0.0364740i
$879$		0			0
$880$	−18168.1	−	10489.4i	−0.695962	−	0.401814i
$881$	−21682.4			−0.829169			−0.414584	−	0.910011i	$-0.636073\pi$
$881$	−21682.4			−0.829169			−0.414584	+	0.910011i	$0.636073\pi$
$882$		0			0
$883$	16034.0			0.611084			0.305542	−	0.952179i	$-0.401162\pi$
$883$	16034.0			0.611084			0.305542	+	0.952179i	$0.401162\pi$
$884$		0			0
$885$		0			0
$886$	−3710.00	−	6425.91i	−0.140677	−	0.243660i
$887$	23410.2	−	40547.7i	0.886176	−	1.53490i	0.0418168	−	0.999125i	$-0.486685\pi$
$887$	23410.2	−	40547.7i	0.886176	−	1.53490i	0.844360	−	0.535777i	$-0.179981\pi$
$888$		0			0
$889$		0			0
$890$		−	41442.1i		−	1.56083i
$891$		0			0
$892$		0			0
$893$	3262.72	−	1883.73i	0.122265	−	0.0705898i
$894$		0			0
$895$		−	2294.55i		−	0.0856964i
$896$		0			0
$897$		0			0
$898$	7270.00	−	12592.0i	0.270159	−	0.467930i
$899$	−15002.8	−	25985.6i	−0.556586	−	0.964034i
$900$		0			0
$901$	19587.5	+	11308.8i	0.724255	+	0.418149i
$902$	4635.69			0.171121
$903$		0			0
$904$	−13024.0			−0.479172
$905$	−47309.4	−	27314.1i	−1.73770	−	1.00326i
$906$		0			0
$907$	−25861.0	−	44792.6i	−0.946748	−	1.63982i	−0.752213	−	0.658920i	$-0.771014\pi$
$907$	−25861.0	−	44792.6i	−0.946748	−	1.63982i	−0.194535	−	0.980896i	$-0.562320\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	38564.2i		−	1.40251i	−0.712909	−	0.701256i	$-0.752623\pi$
$911$		−	38564.2i		−	1.40251i	0.712909	−	0.701256i	$-0.247377\pi$
$912$		0			0
$913$	16464.9	−	9505.99i	0.596831	−	0.344581i
$914$	−8837.76	+	5102.48i	−0.319833	+	0.184655i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−15235.0	+	26387.8i	−0.546851	+	0.947174i	0.451637	+	0.892202i	$0.350840\pi$
$919$	−15235.0	+	26387.8i	−0.546851	+	0.947174i	−0.998488	+	0.0549722i	$0.982493\pi$
$920$	−18542.8	−	32117.0i	−0.664496	−	1.15094i
$921$		0			0
$922$	−3767.82	−	2175.35i	−0.134584	−	0.0777021i
$923$	−9819.23			−0.350167
$924$		0			0
$925$	−58696.0			−2.08639
$926$	4340.50	+	2505.99i	0.154036	+	0.0889329i
$927$		0			0
$928$		0			0
$929$	13222.2	−	22901.6i	0.466962	−	0.808802i	−0.532326	−	0.846540i	$-0.678682\pi$
$929$	13222.2	−	22901.6i	0.466962	−	0.808802i	0.999288	+	0.0377376i	$0.0120151\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	31278.1	−	18058.4i	1.09577	−	0.632643i
$935$	17945.0	−	10360.5i	0.627661	−	0.362380i
$936$		0			0
$937$			19667.6i			0.685711i	0.939388	+	0.342855i	$0.111394\pi$
$937$			19667.6i			0.685711i	−0.939388	+	0.342855i	$0.888606\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1970.17	−	3412.43i	−0.0682525	−	0.118217i	0.829880	−	0.557942i	$-0.188409\pi$
$941$	−1970.17	−	3412.43i	−0.0682525	−	0.118217i	−0.898132	+	0.439726i	$0.855076\pi$
$942$		0			0
$943$	7096.92	+	4097.41i	0.245077	+	0.141495i
$944$	−5394.25			−0.185983
$945$		0			0
$946$	8360.00			0.287322
$947$	45103.7	+	26040.6i	1.54770	+	0.893565i	0.998317	+	0.0579954i	$0.0184709\pi$
$947$	45103.7	+	26040.6i	1.54770	+	0.893565i	0.549384	+	0.835570i	$0.314862\pi$
$948$		0			0
$949$	11988.0	+	20763.8i	0.410060	+	0.710245i
$950$	−40330.5	+	69854.4i	−1.37736	+	2.38566i
$951$		0			0
$952$		0			0
$953$		−	15993.3i		−	0.543626i	−0.962350	−	0.271813i	$-0.912377\pi$
$953$		−	15993.3i		−	0.543626i	0.962350	−	0.271813i	$-0.0876231\pi$
$954$		0			0
$955$	40594.4	−	23437.2i	1.37550	−	0.794146i
$956$		0			0
$957$		0			0
$958$			13111.7i			0.442192i
$959$		0			0
$960$		0			0
$961$	13520.5	−	23418.2i	0.453845	−	0.786083i
$962$	−7754.24	−	13430.7i	−0.259882	−	0.450129i
$963$		0			0
$964$		0			0
$965$	78806.7			2.62889
$966$		0			0
$967$	−24772.0			−0.823799			−0.411900	−	0.911229i	$-0.635135\pi$
$967$	−24772.0			−0.823799			−0.411900	+	0.911229i	$0.635135\pi$
$968$	21340.0	+	12320.6i	0.708566	+	0.409091i
$969$		0			0
$970$	−16872.0	−	29223.2i	−0.558482	−	0.967319i
$971$	27561.3	−	47737.5i	0.910899	−	1.57772i	0.0981028	−	0.995176i	$-0.468723\pi$
$971$	27561.3	−	47737.5i	0.910899	−	1.57772i	0.812797	−	0.582548i	$-0.197944\pi$
$972$		0			0
$973$		0			0
$974$		−	5538.06i		−	0.182188i
$975$		0			0
$976$	−36336.2	+	20978.7i	−1.19169	+	0.688025i
$977$	39109.8	−	22580.0i	1.28069	−	0.739406i	0.303714	−	0.952763i	$-0.401773\pi$
$977$	39109.8	−	22580.0i	1.28069	−	0.739406i	0.976974	+	0.213357i	$0.0684399\pi$
$978$		0			0
$979$		−	10817.2i		−	0.353134i
$980$		0			0
$981$		0			0
$982$	10078.0	−	17455.6i	0.327497	−	0.567241i
$983$	16920.3	+	29306.7i	0.549006	+	0.950906i	0.998343	+	0.0575434i	$0.0183268\pi$
$983$	16920.3	+	29306.7i	0.549006	+	0.950906i	−0.449337	+	0.893362i	$0.648340\pi$
$984$		0			0
$985$	−21858.5	−	12620.0i	−0.707076	−	0.408231i
$986$	22504.2			0.726854
$987$		0			0
$988$		0			0
$989$	12798.6	+	7389.27i	0.411498	+	0.237578i
$990$		0			0
$991$	9191.00	+	15919.3i	0.294613	+	0.510285i	0.974895	−	0.222666i	$-0.0714758\pi$
$991$	9191.00	+	15919.3i	0.294613	+	0.510285i	−0.680282	+	0.732951i	$0.738143\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			16953.6i			0.540166i
$996$		0			0
$997$	−33497.5	+	19339.8i	−1.06407	+	0.614340i	−0.926555	−	0.376160i	$-0.877244\pi$
$997$	−33497.5	+	19339.8i	−1.06407	+	0.614340i	−0.137513	+	0.990500i	$0.543911\pi$
$998$	−25254.2	+	14580.5i	−0.801011	+	0.462464i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.p.a.215.3		8
3.2	odd	2	inner	441.4.p.a.215.2		8
7.2	even	3		63.4.c.b.62.2	yes	4
7.3	odd	6	inner	441.4.p.a.80.2		8
7.4	even	3	inner	441.4.p.a.80.1		8
7.5	odd	6		63.4.c.b.62.1	✓	4
7.6	odd	2	inner	441.4.p.a.215.4		8
21.2	odd	6		63.4.c.b.62.3	yes	4
21.5	even	6		63.4.c.b.62.4	yes	4
21.11	odd	6	inner	441.4.p.a.80.4		8
21.17	even	6	inner	441.4.p.a.80.3		8
21.20	even	2	inner	441.4.p.a.215.1		8
28.19	even	6		1008.4.k.b.881.2		4
28.23	odd	6		1008.4.k.b.881.3		4
84.23	even	6		1008.4.k.b.881.1		4
84.47	odd	6		1008.4.k.b.881.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.c.b.62.1	✓	4	7.5	odd	6
63.4.c.b.62.2	yes	4	7.2	even	3
63.4.c.b.62.3	yes	4	21.2	odd	6
63.4.c.b.62.4	yes	4	21.5	even	6
441.4.p.a.80.1		8	7.4	even	3	inner
441.4.p.a.80.2		8	7.3	odd	6	inner
441.4.p.a.80.3		8	21.17	even	6	inner
441.4.p.a.80.4		8	21.11	odd	6	inner
441.4.p.a.215.1		8	21.20	even	2	inner
441.4.p.a.215.2		8	3.2	odd	2	inner
441.4.p.a.215.3		8	1.1	even	1	trivial
441.4.p.a.215.4		8	7.6	odd	2	inner
1008.4.k.b.881.1		4	84.23	even	6
1008.4.k.b.881.2		4	28.19	even	6
1008.4.k.b.881.3		4	28.23	odd	6
1008.4.k.b.881.4		4	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.44949 + 1.41421i) q^{2} +(-10.5357 + 18.2483i) q^{5} -22.6274i q^{8} +O(q^{10})\)	\(q+(2.44949 + 1.41421i) q^{2} +(-10.5357 + 18.2483i) q^{5} -22.6274i q^{8} +(-51.6140 + 29.7993i) q^{10} +(-13.4722 + 7.77817i) q^{11} -29.7993i q^{13} +(32.0000 - 55.4256i) q^{16} +(31.6070 + 54.7449i) q^{17} +(-77.4209 - 44.6990i) q^{19} -44.0000 q^{22} +(-67.3610 - 38.8909i) q^{23} +(-159.500 - 276.262i) q^{25} +(42.1426 - 72.9932i) q^{26} -125.865i q^{29} +(206.456 - 119.197i) q^{31} +178.796i q^{34} +(92.0000 - 159.349i) q^{37} +(-126.428 - 218.979i) q^{38} +(412.912 + 238.395i) q^{40} -105.357 q^{41} -190.000 q^{43} +(-110.000 - 190.526i) q^{46} +(-21.0713 + 36.4966i) q^{47} -902.268i q^{50} +(309.860 - 178.898i) q^{53} -327.793i q^{55} +(178.000 - 308.305i) q^{58} +(-42.1426 - 72.9932i) q^{59} +(-567.753 - 327.793i) q^{61} +674.282 q^{62} -512.000 q^{64} +(543.787 + 313.955i) q^{65} +(-148.000 - 256.344i) q^{67} -329.512i q^{71} +(-696.788 + 402.291i) q^{73} +(450.706 - 260.215i) q^{74} +(-418.000 + 723.997i) q^{79} +(674.282 + 1167.89i) q^{80} +(-258.070 - 148.997i) q^{82} -1222.14 q^{83} -1332.00 q^{85} +(-465.403 - 268.701i) q^{86} +(176.000 + 304.841i) q^{88} +(-347.677 + 602.193i) q^{89} +(-103.228 + 59.5987i) q^{94} +(1631.36 - 941.866i) q^{95} +566.187i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 256 q^{16} - 352 q^{22} - 1276 q^{25} + 736 q^{37} - 1520 q^{43} - 880 q^{46} + 1424 q^{58} - 4096 q^{64} - 1184 q^{67} - 3344 q^{79} - 10656 q^{85} + 1408 q^{88}+O(q^{100}) \) 8 * q + 256 * q^16 - 352 * q^22 - 1276 * q^25 + 736 * q^37 - 1520 * q^43 - 880 * q^46 + 1424 * q^58 - 4096 * q^64 - 1184 * q^67 - 3344 * q^79 - 10656 * q^85 + 1408 * q^88

Introduction

L-functions

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